Can chiropractic neck "cracking" adjustment reduce dizziness caused by cervical foraminal stenosis?

Not recommended. Neck cracking done as "head thrusts" is considered potentially unsafe and should be avoided. The academy of neurology has come out against this procedure due to high risks of artery dissection and fatal stroke which can occur. I have seen 3 cases of these consequences while in training. I advise all my patients to reconsider doing such maneuvers. Risks vs. Benefits ratio unacceptably high.
Depends upon degree. Dizziness can be caused by feedback (afferentation) due to poorly moving joints which can effect local nerves and the brain. Chiropractic is quite safe, even safer than aspirin, and one might consider various types of chiropractic techniques, such as instrument based techniques (activator, impulse) and with long-standing dizziness unhelped by any other treatment, a functional neurologist.